I do not understand, why these spikes in AND gate output as shown in figure. The AND gate output is just 5V and the MOSFET needs 10 to 12v to trigger.
But this circuit is working. The gate driver output is 10v. Is the gate driver is having pull up voltage capacity?.

I do not understand, why these spikes in AND gate output as shown in figure. The AND gate output is just 5V and the MOSFET needs 10 to 12v to trigger.
But this circuit is working. The gate driver output is 10v. Is the gate driver is having pull up voltage capacity?.

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What gate driver is U1/U2? Why is there no gate resistance?
You say "output of AND gate". Your graphs show "Vg". Which signal is it?